The easiest way to solve this equation is by graphing.

To solve a system of equations, you can use 2 methods. You can, one, graph the equations and find the intersection, or two, eliminate a variable.

1. Graphing: we can put the two equations in standard form, or y=mx+b, with m being the slope and b being the y-intercept. So, your two equations are y=x-3 and y=-x+5.

We can see the intersection is (4,1), so x=4 and y=1.

2. Elimination: We can try to eliminated one of the variables, solve for the other, and plug that back in to solve for the other. In this case, let's try to eliminate x.

x-y=3

x+y=5

By subtracting these equations from each other, since x-x=0, -y-y=-2y, and 3-5=-2, our new equation becomes 0-2y=-2. If we divide both sides by -2, we get y=1. We can then take any of the original equations, x-y=3, and plug it in. So, x-(1)=3, so x=4.